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  <div class="section" id="numpy-polynomial-laguerre-lagroots">
<h1>numpy.polynomial.laguerre.lagroots<a class="headerlink" href="#numpy-polynomial-laguerre-lagroots" title="Permalink to this headline">¶</a></h1>
<dl class="function">
<dt id="numpy.polynomial.laguerre.lagroots">
<code class="sig-prename descclassname">numpy.polynomial.laguerre.</code><code class="sig-name descname">lagroots</code><span class="sig-paren">(</span><em class="sig-param">c</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/numpy/numpy/blob/v1.18.1/numpy/polynomial/laguerre.py#L1424-L1481"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#numpy.polynomial.laguerre.lagroots" title="Permalink to this definition">¶</a></dt>
<dd><p>Compute the roots of a Laguerre series.</p>
<p>Return the roots (a.k.a. “zeros”) of the polynomial</p>
<div class="math">
<p><img src="../../_images/math/0f474ea08a4acdec419ca474e58369291d12793b.svg" alt="p(x) = \sum_i c[i] * L_i(x)."/></p>
</div><dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>c</strong><span class="classifier">1-D array_like</span></dt><dd><p>1-D array of coefficients.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>out</strong><span class="classifier">ndarray</span></dt><dd><p>Array of the roots of the series. If all the roots are real,
then <em class="xref py py-obj">out</em> is also real, otherwise it is complex.</p>
</dd>
</dl>
</dd>
</dl>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><code class="xref py py-obj docutils literal notranslate"><span class="pre">polyroots</span></code>, <code class="xref py py-obj docutils literal notranslate"><span class="pre">legroots</span></code>, <code class="xref py py-obj docutils literal notranslate"><span class="pre">chebroots</span></code>, <code class="xref py py-obj docutils literal notranslate"><span class="pre">hermroots</span></code>, <code class="xref py py-obj docutils literal notranslate"><span class="pre">hermeroots</span></code></p>
</div>
<p class="rubric">Notes</p>
<p>The root estimates are obtained as the eigenvalues of the companion
matrix, Roots far from the origin of the complex plane may have large
errors due to the numerical instability of the series for such
values. Roots with multiplicity greater than 1 will also show larger
errors as the value of the series near such points is relatively
insensitive to errors in the roots. Isolated roots near the origin can
be improved by a few iterations of Newton’s method.</p>
<p>The Laguerre series basis polynomials aren’t powers of <em class="xref py py-obj">x</em> so the
results of this function may seem unintuitive.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">numpy.polynomial.laguerre</span> <span class="kn">import</span> <span class="n">lagroots</span><span class="p">,</span> <span class="n">lagfromroots</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">coef</span> <span class="o">=</span> <span class="n">lagfromroots</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">coef</span>
<span class="go">array([  2.,  -8.,  12.,  -6.])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">lagroots</span><span class="p">(</span><span class="n">coef</span><span class="p">)</span>
<span class="go">array([-4.4408921e-16,  1.0000000e+00,  2.0000000e+00])</span>
</pre></div>
</div>
</dd></dl>

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